Here’s a simple idea I bet most Americans agree with: No qualified high school student should ever be barred entrance to a college based on his or her family’s bank account. Yet it happens all the time.

When colleges review applications, all but a few consider a student’s ability to pay. As a result, high-achieving applicants from low- and middle-income families are routinely denied seats that are saved for students whose families have deeper pockets. This hurts the son of a farmer in Nebraska as much as the daughter of a working mother in Detroit.